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RRDGRAPH_RPN(1)                     rrdtool                    RRDGRAPH_RPN(1)

       rrdgraph_rpn - About RPN Math in rrdtool graph

       RPN expression:=vname|operator|value[,RPN expression]

       If you have ever used a traditional HP calculator you already know RPN (Reverse Polish Notation).  The idea
       behind RPN is that you have a stack and push your data onto this stack. Whenever you execute an operation, it
       takes as many elements from the stack as needed. Pushing is done implicitly, so whenever you specify a number
       or a variable, it gets pushed onto the stack automatically.

       At the end of the calculation there should be one and only one value left on the stack.  This is the outcome of
       the function and this is what is put into the vname.  For CDEF instructions, the stack is processed for each
       data point on the graph. VDEF instructions work on an entire data set in one run. Note, that currently VDEF
       instructions only support a limited list of functions.

       Example: "VDEF:maximum=mydata,MAXIMUM"

       This will set variable "maximum" which you now can use in the rest of your RRD script.

       Example: "CDEF:mydatabits=mydata,8,*"

       This means:  push variable mydata, push the number 8, execute the operator *. The operator needs two elements
       and uses those to return one value.  This value is then stored in mydatabits.  As you may have guessed, this
       instruction means nothing more than mydatabits = mydata * 8.  The real power of RPN lies in the fact that it is
       always clear in which order to process the input.  For expressions like "a = b + 3 * 5" you need to multiply 3
       with 5 first before you add b to get a. However, with parentheses you could change this order: "a = (b + 3) *
       5". In RPN, you would do "a = b, 3, +, 5, *" without the need for parentheses.

       Boolean operators
           LT, LE, GT, GE, EQ, NE

           Pop two elements from the stack, compare them for the selected condition and return 1 for true or 0 for
           false. Comparing an unknown or an infinite value will result in unknown returned ... which will also be
           treated as false by the IF call.

           UN, ISINF

           Pop one element from the stack, compare this to unknown respectively to positive or negative infinity.
           Returns 1 for true or 0 for false.


           Pops three elements from the stack.  If the element popped last is 0 (false), the value popped first is
           pushed back onto the stack, otherwise the value popped second is pushed back. This does, indeed, mean that
           any value other than 0 is considered to be true.

           Example: "A,B,C,IF" should be read as "if (A) then (B) else (C)"

       Comparing values
           MIN, MAX

           Pops two elements from the stack and returns the smaller or larger, respectively.  Note that infinite is
           larger than anything else.  If one of the input numbers is unknown then the result of the operation will be
           unknown too.


           Pops two elements from the stack and uses them to define a range.  Then it pops another element and if it
           falls inside the range, it is pushed back. If not, an unknown is pushed.

           The range defined includes the two boundaries (so: a number equal to one of the boundaries will be pushed
           back). If any of the three numbers involved is either unknown or infinite this function will always return
           an unknown

           Example: "CDEF:a=alpha,0,100,LIMIT" will return unknown if alpha is lower than 0 or if it is higher than

           +, -, *, /, %

           Add, subtract, multiply, divide, modulo


           NAN-safe addition. If one parameter is NAN/UNKNOWN it'll be treated as zero. If both parameters are
           NAN/UNKNOWN, NAN/UNKNOWN will be returned.

           SIN, COS, LOG, EXP, SQRT

           Sine and cosine (input in radians), log and exp (natural logarithm), square root.


           Arctangent (output in radians).


           Arctangent of y,x components (output in radians).  This pops one element from the stack, the x (cosine)
           component, and then a second, which is the y (sine) component.  It then pushes the arctangent of their
           ratio, resolving the ambiguity between quadrants.

           Example: "CDEF:angle=Y,X,ATAN2,RAD2DEG" will convert "X,Y" components into an angle in degrees.

           FLOOR, CEIL

           Round down or up to the nearest integer.

           DEG2RAD, RAD2DEG

           Convert angle in degrees to radians, or radians to degrees.


           Take the absolute value.

       Set Operations
           SORT, REV

           Pop one element from the stack.  This is the count of items to be sorted (or reversed).  The top count of
           the remaining elements are then sorted (or reversed) in place on the stack.

           Example: "CDEF:x=v1,v2,v3,v4,v5,v6,6,SORT,POP,5,REV,POP,+,+,+,4,/" will compute the average of the values
           v1 to v6 after removing the smallest and largest.


           Pop one element (count) from the stack. Now pop count elements and build the average, ignoring all UNKNOWN
           values in the process.

           Example: "CDEF:x=a,b,c,d,4,AVG"

           TREND, TRENDNAN

           Create a "sliding window" average of another data series.

           Usage: CDEF:smoothed=x,1800,TREND

           This will create a half-hour (1800 second) sliding window average of x.  The average is essentially
           computed as shown here:

                                  delay     t0
                                    delay       t1
                                         delay      t2

                Value at sample (t0) will be the average between (t0-delay) and (t0)
                Value at sample (t1) will be the average between (t1-delay) and (t1)
                Value at sample (t2) will be the average between (t2-delay) and (t2)

           TRENDNAN is - in contrast to TREND - NAN-safe. If you use TREND and one source value is NAN the complete
           sliding window is affected. The TRENDNAN operation ignores all NAN-values in a sliding window and computes
           the average of the remaining values.


           Create a "sliding window" average/sigma of another data series, that also shifts the data series by given
           amounts of of time as well

           Usage - explicit stating shifts: CDEF:predict=<shift n>,...,<shift 1>,n,<window>,x,PREDICT
           CDEF:sigma=<shift n>,...,<shift 1>,n,<window>,x,PREDICTSIGMA

           Usage - shifts defined as a base shift and a number of time this is applied CDEF:predict=<shift
           multiplier>,-n,<window>,x,PREDICT CDEF:sigma=<shift multiplier>,-n,<window>,x,PREDICTSIGMA

           Example: CDEF:predict=172800,86400,2,1800,x,PREDICT

           This will create a half-hour (1800 second) sliding window average/sigma of x, that average is essentially
           computed as shown here:

                                                             shift 1        t0
                                                  shift 2
                                                                 shift 1        t1
                                                       shift 2

            Value at sample (t0) will be the average between (t0-shift1-window) and (t0-shift1)
                                                 and between (t0-shift2-window) and (t0-shift2)
            Value at sample (t1) will be the average between (t1-shift1-window) and (t1-shift1)
                                                 and between (t1-shift2-window) and (t1-shift2)

           The function is by design NAN-safe.  This also allows for extrapolation into the future (say a few days) -
           you may need to define the data series whit the optional start= parameter, so that the source data series
           has enough data to provide prediction also at the beginning of a graph...

           Here an example, that will create a 10 day graph that also shows the prediction 3 days into the future with
           its uncertainty value (as defined by avg+-4*sigma) This also shows if the prediction is exceeded at a
           certain point.

           rrdtool graph image.png --imgformat=PNG \
            --start=-7days --end=+3days --width=1000 --height=200 --alt-autoscale-max \
            DEF:value=value.rrd:value:AVERAGE:start=-14days \
            LINE1:value#ff0000:value \
            CDEF:predict=86400,-7,1800,value,PREDICT \
            CDEF:sigma=86400,-7,1800,value,PREDICTSIGMA \
            CDEF:upper=predict,sigma,3,*,+ \
            CDEF:lower=predict,sigma,3,*,- \
            LINE1:predict#00ff00:prediction \
            LINE1:upper#0000ff:upper\ certainty\ limit \
            LINE1:lower#0000ff:lower\ certainty\ limit \
            CDEF:exceeds=value,UN,0,value,lower,upper,LIMIT,UN,IF \

           Note: Experience has shown that a factor between 3 and 5 to scale sigma is a good discriminator to detect
           abnormal behavior. This obviously depends also on the type of data and how "noisy" the data series is.

           This prediction can only be used for short term extrapolations - say a few days into the future-

       Special values

           Pushes an unknown value on the stack

           INF, NEGINF

           Pushes a positive or negative infinite value on the stack. When such a value is graphed, it appears at the
           top or bottom of the graph, no matter what the actual value on the y-axis is.


           Pushes an unknown value if this is the first value of a data set or otherwise the result of this CDEF at
           the previous time step. This allows you to do calculations across the data.  This function cannot be used
           in VDEF instructions.


           Pushes an unknown value if this is the first value of a data set or otherwise the result of the vname
           variable at the previous time step. This allows you to do calculations across the data. This function
           cannot be used in VDEF instructions.


           Pushes the number 1 if this is the first value of the data set, the number 2 if it is the second, and so
           on. This special value allows you to make calculations based on the position of the value within the data
           set. This function cannot be used in VDEF instructions.

           Time inside RRDtool is measured in seconds since the epoch. The epoch is defined to be
           "Thu Jan  1 00:00:00 UTC 1970".


           Pushes the current time on the stack.


           Pushes the time the currently processed value was taken at onto the stack.


           Takes the time as defined by TIME, applies the time zone offset valid at that time including daylight
           saving time if your OS supports it, and pushes the result on the stack.  There is an elaborate example in
           the examples section below on how to use this.

       Processing the stack directly
           DUP, POP, EXC

           Duplicate the top element, remove the top element, exchange the two top elements.

       These operators work only on VDEF statements. Note that currently ONLY these work for VDEF.

           Return the corresponding value, MAXIMUM and MINIMUM also return the first occurrence of that value in the
           time component.

           Example: "VDEF:avg=mydata,AVERAGE"

           Returns the standard deviation of the values.

           Example: "VDEF:stdev=mydata,STDEV"

       LAST, FIRST
           Return the last/first non-nan or infinite value for the selected data stream, including its timestamp.

           Example: "VDEF:first=mydata,FIRST"

           Returns the rate from each defined time slot multiplied with the step size.  This can, for instance, return
           total bytes transferred when you have logged bytes per second. The time component returns the number of

           Example: "VDEF:total=mydata,TOTAL"

           This should follow a DEF or CDEF vname. The vname is popped, another number is popped which is a certain
           percentage (0..100). The data set is then sorted and the value returned is chosen such that percentage
           percent of the values is lower or equal than the result.  For PERCENTNAN Unknown values are ignored, but
           for PERCENT Unknown values are considered lower than any finite number for this purpose so if this operator
           returns an unknown you have quite a lot of them in your data.  Infinite numbers are lesser, or more, than
           the finite numbers and are always more than the Unknown numbers.  (NaN < -INF < finite values < INF)

           Example: "VDEF:perc95=mydata,95,PERCENT"

           Return the parameters for a Least Squares Line (y = mx +b) which approximate the provided dataset.
           LSLSLOPE is the slope (m) of the line related to the COUNT position of the data.  LSLINT is the y-intercept
           (b), which happens also to be the first data point on the graph. LSLCORREL is the Correlation Coefficient
           (also know as Pearson's Product Moment Correlation Coefficient).  It will range from 0 to +/-1 and
           represents the quality of fit for the approximation.

           Example: "VDEF:slope=mydata,LSLSLOPE"

       rrdgraph gives an overview of how rrdtool graph works.  rrdgraph_data describes DEF,CDEF and VDEF in detail.
       rrdgraph_rpn describes the RPN language used in the ?DEF statements.  rrdgraph_graph page describes all of the
       graph and print functions.

       Make sure to read rrdgraph_examples for tips&tricks.

       Program by Tobias Oetiker <>

       This manual page by Alex van den Bogaerdt <> with corrections and/or additions by several

1.4.7                             2012-01-18                   RRDGRAPH_RPN(1)